"In these shoes? I doubt you'd survive."
So shoes may not be something you really consider when you're focusing on health but it's ridiculous what the quality of footwear can do for your exercise regimine.
Obviously it will matter what you're doing (running, biking, etc) but even more that you're going to want to make sure you're accommodating your foot type as much as possible. Me? I'm a freaking hobbit. My feet are large for my height, they're flat and my ankles occasionally like to try to give me the slip. So I make sure my running shoes properly support that. Flat shoes are a no-no here when it comes to the inside of your shoe. Don't go running in your converse! You need arch and ankle support.
There are places like Runner's World who offer an online shoe adviser but if you ask around you can find someone local to you who can help fit you to the right shoe.
Despite the fairly impractical outfits we've seen Lara in over the years, they have oddly kept fairly sensible footwear. Even in Tomb Raider: Legends when in the evening gown, she kicked off the heels and climbed barefoot.
Just remember you only have two legs to stand on and those legs are always supported by your feet--so if you take care of them when you work out, they'll take care of you.